The Equitable Adjacent Strong Edge Colorings Of Some Graphs

The Equitable adjacent strong edge colorings of graphs is a important field of graph and is widely applied in computer and network problem.This paper discusses the Equitable adjacent strong edge colorings of graphs.The Equitable adjacent strong chromatic number is denoted byχ'_eas(G).About Equitable adjacent strong edge colorings of graphs, Zhang Zhongfu made a following conjecture :for any connected graphG with|V(G)|≥3,thenâ–³(G)≤χ'_eas(G)≤△(G) + 2 G≠C₅.In Chapter one,I study the equitable adjacent colorings of P₃×C_n.In Chapter two,we study the equitable adjacent strong edge colorings of some ex-tenged Mycielski graphs and give the equitable adjacent strong edge chromatic number of some extended Mycielski graphs.In Chapter three, we prove study the equitable adjacent strong edge colorings ofθ-graph,give the equitable adjacent strong chromatic number ofθ-graph.the following many results:Theorem 1 For P_n(n≥2),V(P_n) = {u₁,u₂,...,u_n},Theorem 2 For C_n(n≥3), V(C_n) = {v₁,v2,..., v_n},Theorem 3 For S_n(K_1,n), V(S_n) = {V₀, V₁,..., V_n},Theorem 4 Forω_n,when n≥3, Theorem 5 For F_n,when n≥3,2n≤χ'_eas(M(F_n))≤2n+1...